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Blocked-Braid Groups

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Abstract

We introduce and study a family of groups BB n , called the blocked-braid groups, which are quotients of Artin’s braid groups B n , and have the corresponding symmetric groups Σ n as quotients. They are defined by adding a certain class of geometrical modifications to braids. They arise in the study of commutative Frobenius algebras and tangle algebras in braided strict monoidal categories. A fundamental equation true in BB n is Dirac’s Belt Trick - that torsion through 4π is equal to the identity. We show that BB n is finite for n = 1, 2 and 3 but infinite for n > 3.

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Authors and Affiliations

  1. Dipartimento di Scienza e Alta Tecnologia, Università dell’ Insubria, via Carloni, 78, Como, Italy

    D. Maglia, N. Sabadini & R. F. C. Walters

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  1. D. Maglia
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  2. N. Sabadini
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  3. R. F. C. Walters
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Correspondence to R. F. C. Walters.

Additional information

Dedicated to George Janelidze on the occasion of his sixtieth birthday.

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Maglia, D., Sabadini, N. & Walters, R.F.C. Blocked-Braid Groups. Appl Categor Struct 23, 53–61 (2015). https://doi.org/10.1007/s10485-013-9363-2

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  • DOI: https://doi.org/10.1007/s10485-013-9363-2

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